23 – Over 100 Pages of Chem Worksheets — Free!

For instructors in College General Chemistry or Preparatory Chemistry — or HS Honors or AP Chem — we offer over 100 pages of student assignments that can be used either in-class or as self-study homework. These individual assignments review and teach fundamentals of chemistry calculations — and the math pre-requisite for these topics.

Included is access for instructors to short quizzes on the assignments.

And it is all absolutely FREE.  Try a few with your students.  Send us a comment on how they do!



22 – Updating Johnstone

The peer-reviewed journal Foundations of Chemistry has published “Improving student success in chemistry through cognitive science” by Dr. JudithAnn Hartman, Eric Nelson, and Dr. Paul Kirschner.  The content is open access and available for free.

The article is a review and update of the work of the chemistry educator Alex Johnstone, whose interest was how the brain of student learners solves chemistry problems.

Readers are invited to leave responses and questions in the comments section of this post.


21 – Gaining Automaticity in Vocabulary Recall

Looking for a way to speed student learning, increase problem-solving skill, and improve retention of knowledge students learn?

Cognitive experts predict learning will be accelerated if at the start of a new topic, students gain “automaticity” in recalling the definitions of new vocabulary.

Below we’ve posted an assignment that helps students learn initial electrochemistry vocabulary during homework.  The assignment takes 10 minutes of class time but frees up 1-2 in-class hours for electrochem demonstrations and problem solving.

Quizzes are included to encourage homework completion, and cognitive science supporting vocab automaticity is discussed.

Helping students gain automaticity in recall of fundamentals is strongly supported by cognitive research — but experiments and tweaks are always required to adapt science to unique classroom conditions.  Will “text-based homework and quiz” work for your students?


20 – An Acid-Base Math Review

At the point you are about to teach  [H+] and [OH-] in strong acid and base solutions, here’s an experiment you might try that takes only 10 minutes of class time — and may yield interesting results.

Cognitive science advises that, when teaching how to solve chem calculations,

  • if before a new topic is started, students are given review of just the number-math encountered in topic problems, and
  • if that practice uses simple numbers that students can solve by mental arithmetic,

when the chem component is added, both the math operations and chemistry will be learned more quickly — and better retained.

In practice, with real students, might science be right?

As an experiment, at  https://www.ChemReview.Net/pdfs/ABMathToInstructors.pdf  is an assignment that teaches students the math of calculating [H+] and [OH-] in acidic and basic solutions — without a calculator — as a homework assignment.

The homework provides worked out answers.   For instructors, quiz questions and citations on the cognitive science are included.

It’s an experiment in the science of learning that may help us learn how students can better learn and retain chem – and it requires only 2 minutes of class time.  Worth a try?

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19 – Video on “How to Learn” from Stephen Chew

Cognitive scientist Dr. Stephen Chew has posted a 24-minute video on “How to Learn in Pandemic Times”  addressing how students can overcome fundamental bottlenecks in learning.  For instructors, it’s a great summary of how we can help students — during Covid times and thereafter.

For several years, Dr. Judy Hartman from the USNA Chemistry faculty and Eric Nelson have been working to prepare research summaries that explained to chemistry and physics educators how  cognitive science describes how the student brain solves problems and learns to solve problems.  The hope has been that with knowledge of this science, instructors can improve student success rates in STEM majors.  Our latest effort has been the article “A Praradigm Shift:  Implications of Working Memory Limits,” posted at  http://arxiv.org/abs/2102.00454 and discussed in Post 18.

Working independently to explain the science to a broader educator audience, cognitive expert Dr. Chew came up with what looks to be the same explanation we did, in fewer words and  great graphics.  Having degrees in chemistry, not cognitive science, we were relieved to watch the expert’s description of importance of the working memory bottleneck — and how automaticity achieved by over-learning can circumvent the bottleneck and speed the rate of learning.

Dr. Chew’s video explains fundamental principles that can guide instructors in designing instruction and students in learning how to learn.  As homework to help  your students understand learning, you might consider this:

“Assignment:  Watch the 24 minute video on making study more effective — at


“Be ready to answer the 8 Review Questions at the end  (either)  in a quiz on [date] ( or )  as part of the next quiz on (topic).”

Two questions you might add in a brief discussion of the video:

“Why it is important to turn off your cell phone during study if you want to major in science?


“What is overlearning and why is it important?”

For citations of the cognitive research supporting the video , see the article on “Working Memory Limits” discussed in Post 18.

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18 – Working Memory Limits and Chemistry and Physics Instruction

Dr. JudithAnn Hartman and Eric Nelson have a new research summary:

“A Paradigm Shift: The Implications of Working Memory Limits for Physics and Chemistry Instruction” 

We hope it may be helpful to instructors in courses for majors in the sciences or engineering.

The intent of this “preprint” is to invite critical feedback — which may be left in the comments section of this post.

This article is an update of our 2014 paper “‘Do We Need to Memorize That?’ Or Cognitive Science for Chemists.”  In the past six years, extensive new research has been published by cognitive neuroscientists on issues in science instruction.

One key finding: According to the consensus of cognitive experts, students in introductory courses for science majors can only reliably solve the kind of problems at the end of the chapter in most textbooks by applying well-memorized algorithms  that apply well-memorized facts.

This is likely not what any of us wanted to hear, but science is not required to heed our preferences.

Cognitive experts say conceptual understanding is the right goal, but it takes quite a bit of thorough memorization to achieve.

And, even if concepts are understood, because of the brain’s working memory limits, to solve problems of any complexity, students still must memorize the fundamental facts and algorithms that their instructors recommend they overlearn — which means memorize so they can be recalled perfectly, repeatedly.

Chem ed journals often deprecate memorization and algorithmic problem solving, but on questions of how the brain works, it may be wise to defer to those whose scientific expertise is the study of how the brain works.

The cognitive experts say, to learn each new topic, students must start with initial and thorough memorization of fundamental vocabulary, facts, and relationships identified by their instructors, followed by problem solving using their new recallable fundamentals to solve problems in a variety of distinctive contexts, including word problems, demonstrations, labs, and simulations.



17 – Science Says: Speed in Factual Recall Matters

In a recent online opinion column in Education Week (1/13/2020), math education professor Jo Boaler writes that her paper “Fluency Without Fear … builds a case … on the importance of moving away from speed and memorization toward number sense and conceptual thinking.”

But in fact, what scientists say about memorization and speed is the opposite of what Boaler claims.

The key surprising discovery of cognitive science in recent research:  When solving problems, the human brain has remarkable strengths but also stringent limitations.   Scientists have verified that during the steps of solving a problem,  “working memory” (where your brain solves problems) has an essentially unlimited ability to apply facts and procedures that can be quickly recalled from long-term memory.

However, at each problem step, working memory can generally hold only 3-5 “chunks” of not-well-memorized data and relationships, each for 30 seconds or less (Cowan 2000, 2010; Clark, Sweller, and Kirschner, Spring 2012).

This makes memorization a key part of math (and chem and physics) success. When solving a multi-step problem, if needed relationships must be looked up, calculated on a calculator, or even mentally calculated, storing the answer takes up space that is limited in working memory. This tends to overload working memory, problem data tends to drop out, and confusion tends to result.

Cognitive scientist Susan Gathercole advises  to “avoid working memory overload in structured learning activities.” She explains:

“The capacity of working memory is limited, and the imposition of either excess storage or processing demands in the course of an on-going cognitive activity will lead to catastrophic loss of information from this temporary memory system.” (Working Memory in the Classroom, 2008)

How can the brain work around working memory limits?

In 2008, a U.S. Presidential Commission reported on ways to improve education in fields that rely upon math.  Six leading cognitive scientists  wrote that to get around the “bottleneck” of working memory’s limitations, the “central” strategy is

“the achievement of automaticity, that is, the fast, implicit, and automatic retrieval of a fact or a procedure from long-term memory.” (Geary et al., . Report of the NMAP Task Force on Learning Processes , page 4-5)

So what students need, say the experts, is fast recall of memorized facts and procedures.  How is this recall achieved?  By exerting effort to memorize. In their task force report, the cognitive scientists noted:

“Verbatim recall of math knowledge is an essential feature of math education, and it requires a great deal of time, effort, and practice.” (p. 4-xii)

Cognitive scientist Daniel Willingham explains:

“Does speed matter? It does. When working a complex problem you not only want to pull simple math facts from memory, you want to do so quickly, so that the other work can proceed apace. Indeed, adults with stronger higher-level math achievement retrieve math facts faster (Hecht, 1999).” (Science and Education blog, 7/2/2017)

Boaler claims “conceptual thinking” can take the place of “speed and memorization.” But scientists tell us that in the brain, to construct conceptual frameworks, small chunks of new knowledge first must be stored in the neurons of long-term memory:  “memorized” by effort at recall. Neurons gradually wire together if the knowledge they hold is repeatedly recalled at the same time at steps during problem solving. (Hebb, 1949).

But connections do not grow between empty neurons. Willingham writes:

“A teacher cannot pour concepts directly into students’ heads. Rather, new concepts must build on something students already know.” (American Educator, Winter 2009-10)

Boaler claims students can learn math without the hard work involved in memorizing fundamentals. Perhaps she is “influential” because that’s what we would all prefer to hear.  No one wants Dickensian schools.

But scientists say what she is advocating simply does not work.  How the brain works in the ways science says it works.

Unless teachers ask students to exert the effort needed to achieve quick recall of fundamental facts and procedures, according to science, students will be severely handicapped in their ability to solve math problems above grades K-3, when problems involve more steps. 

Education Week has been publishing a series of articles on “The Science of Reading.”  It’s been incredibly informative for educators seeking to improve student learning. I do not, however, recall any article which covered the consensus of science on how students can and cannot learn math.

In math, they have chosen to publish views that deny science.  Do such views merit publication?  Would an education journal publish a column by those who argue against vaccination before students are enrolled in school?

As professionals, we as educators have a moral and legal obligation to do our best to follow scientific best practices. If we listen to science on the importance of memorization and speed in recall, student prospects in careers that require math will rise. Poor and minority children will especially benefit.

16 – Online Conference: Help with the Math of Chemistry

NSF data tell us that nationally, about 90% of students who take science-major college chemistry hope to major in biology, health sciences, or engineering.  Those majors require first-year chemistry because molecular behavior is a foundation for all science, but also with the expectation that chemistry will teach calculation skills that are central in scientific disciplines.

In scientific calculations, numbers have units attached. In addition, if equations are required, students are expected to determine which data goes where, and in chemistry, students learn to do so.  But most chemistry textbooks optimistically assume that students during K-12 have learned the fundamental rules of arithmetic and algebraic computation.

In the U.S. for the current generation, due to circumstances often beyond their control, test data show that computation skills have declined substantially since about 1990.  We also we know from cognitive studies (but did not know until recently) that to solve calculations reliably, students need “very high” rather than “moderate” proficiency in math computation.   And because over-reliance on calculators and a decrease in calculation practice have been a part of K-12 math standards in most states since 1990, current students leaving K-12 are unlikely to have “very high” computational proficiency.

These issues are discussed in some detail in the paper

Addressing Math Deficits to Improve Chemistry Success



This was one of eight papers presented and discussed in the fall of 2017 at an ACS Division of Chemical Education (DivChEd) online conference on “Improving Student Skills in the Mathematics of Chemistry.” Among the topics:

  • Papers 1 and 4 discussed the benefits, procedures, and tips for teaching both first-year and Physical Chemistry without a calculator. These strategies encourage students to use “mental math” to both estimate as a check calculator answers and strengthen the sense of numeracy that helps with conceptual understanding.  Those papers are at:

Paper 1:   https://confchem.ccce.divched.org/2017fallconfchemp1

Paper 4:  https://confchem.ccce.divched.org/content/2017fallconfchemp4

  • A Texas study found that the better first semester general chemistry students did on a test early in the semester of simple “chem math” without a calculator, the better their semester grade tended to be, but the better they did on the same test with a calculator, the worse on average was their semester grade.

These data support the cognitive science prediction that as a basis for placement into “prep chem” vs. “gen chem,” a test of math without a calculator is a better predictor of which students need additional preparation for chemistry.

They also suggest the importance of mental math review as preparation for college chemistry.

Paper 2:  https://confchem.ccce.divched.org/content/2017fallconfchemp2

  • ACS Exam results reported in Paper 5  indicate that students who are given a review of math “just in time” for topics in general chemistry can show substantial gains in achievement, but gains are more likely to be seen for students whose math preparation is “average or above.”  These data suggest that students with below average math scores may need more preparation in math than a “during gen chem class and homework” review can provide.

Paper 5:  https://confchem.ccce.divched.org/content/2017fallconfchemp5

  • Papers 3, 6, and 7 provide additional evidence that a review of pre-requisite math prior to or concurrent with topics in chemistry has a positive impact on chemistry achievement. See:


I believe you will find a wealth of stimulating ideas in these papers for your own experiments to improve student success.

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15 – Needed: A Cognitive Fix for Math Standards

Posted below is an analysis of the alignment of the K-12 Common Core Math Standards (CCMS) (and state math standards similar to the Common Core) with the findings of recent cognitive research.

What does this have to do with Chemistry?  Chemistry is a quantitative science, and the goal of the ChemReview project since 2006 has been to help students with the math needed to succeed in quantitative science courses.  It was hoped that with the adoption in most states of CCMS-type standards, such help for students would no longer be needed, because students would arrive in first-year chemistry with the essential mastery of pre-requisite math fundamentals.  The analysis in the paper above finds this did not happen.  Though the CCMS are superior in some areas to previous math standards in most states, in many key areas the CCMS ask students to solve problems in ways that science says the human brain simply cannot do.

Click to access CCMS.pdf

Comments on the paper are most welcome.  If a comment form does not appear below this posting, click on the word “comment” below the title of this post.

14 – Math Computation and Student Success in Science Courses

The paper “Automaticity in Computation and Student Success in Introductory Physical Science Courses” is available as a PDF from the ArXiv site at no cost.

The article compares US math standards in place in most states until about 2012 (with impact on most current US students) to the recent findings of cognitive science on how the student brain solves problems.  The impact of those standards on student preparation for quantitative science courses is discussed.


Authors Dr. JudithAnn Hartman and Eric Nelson welcome comments, corrections, opposing and/or additional viewpoints.